Polynomial Division Calculator



This calculator can be used to obtain the quotient of a division of polynomials. If the division is not exact, the remainder will also be displayed.

How to use the polynomial division calculator?

Step 1: Enter the polynomial that is the dividend of the division in the first input box. Use * to indicate multiplication between variables and coefficients. For example, enter 4*x or 3*x^2, instead of 4x or 3x^2.

Step 2: Enter the polynomial that is the divisor in the second input box.

Step 3: Click “Divide” to get the solution to the division.

Step 4: The solution along with the original polynomials will be displayed at the bottom.

How to enter polynomials in the calculator?

To enter polynomials correctly, we must consider several aspects. First, it is important to use * to indicate multiplication between variables and coefficients. This means that instead of entering 2x or 8x, we must enter 2*x or 8*x.

Additionally, we can use the ^ sign to write exponents. For example, we can indicate the exponent \(x^3\), by writing x^3.

Lastly, we can also use fractional coefficients using the / sign. For example, 1/2*x indicates a half of x.

The following are some examples of how to enter polynomials correctly:

  • To write \(x^3+2x+3\), enter x^3+2*x+3.
  • To write \(4x^2-3x+7\), enter 4*x^2-3*x+7.
  • To write \(\frac{1}{2}x^3-\frac{1}{3}x^2+2x\), enter 1/2*x^3-1/3*x^2+2*x.

Does the division need to be exact?

No, it is not necessary. If the polynomial division is not exact, then the calculator will return the remainder along with the quotient. The remainder will be displayed as a fraction where the numerator is the remainder and the denominator is the divisor.

For example, suppose that in a division where x+1 is the divisor, we obtain a quotient equal to \(x^2+3\) and a remainder equal to 5. Then, the calculator will display the result \(x^2 +3+\frac{5}{x+1}\).

How to divide polynomials manually?

To divide polynomials manually, we follow these steps:

  1. We write the polynomial in descending order. If there is a missing term, we leave a blank space.
  2. We divide the term with the highest power in the dividend by the term with the highest power in the divisor.
  3. We multiply the answer obtained in the previous step by the divisor.
  4. We subtract what is obtained and write the following term.
  5. We repeat steps 2, 3, and 4 until there are no more terms left.
  6. We write the final answer. The remaining term after subtracting the last terms is the remainder. We write the remainder as a fraction where the divisor is the denominator.

If you want to learn more about dividing polynomials, you can visit our polynomial division with examples article.

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